Hoisting apparatus for handling with coil of wires

Import 21/11/2008Prezenční342 - Institut dopravyNeuveden

Clam-shel brake of load lift

Prezenční342 - Institut doprav

Nonstationary Extrapolated Modulus Algorithms for the solution of the Linear Complementarity Problem

The Linear Complementarity Problem (LCP) has many applications as, e.g., in the solution of Linear and Convex Quadratic Programming, in Free Boundary Value problems of Fluid Mechanics, etc. In the present work we assume that the matrix coefficient M is an element of R(n,n) of the LCP is symmetric positive definite and we introduce the (optimal) nonstationary extrapolation to improve the convergence rates of the well-known Modulus Algorithm and Block Modulus Algorithm for its solution. Two illustrative numerical examples show that the (Optimal) Nonstationary Extrapolated Block Modulus Algorithm is far better than all the previous similar Algorithms. (C) 2009 Elsevier Inc. All rights reserved

The principle of extrapolation and the Cayley Transform

The Cayley Transform, F := (I + A)(-1)(I - A), with A is an element of C-n,C-n and -1 is not an element of sigma (A), where sigma(.) denotes spectrum, is of significant theoretical importance and interest and has many practical applications. E.g., in the solution of the Linear Complementarity Problem (LCP), in the solution of linear systems arising from the discretization of model problems elliptic PDEs by Alternating Direction Implicit (ADI) iterative methods, in the solution of complex linear systems by ADI-type methods of Hermitian/Skew Hermitian or Normal/Skew Hermitian Splittings, etc. In the present work we apply the principle of Extrapolation to generalize the Cayley Transform and determine in an optimal sense the Extrapolation parameter involved so that problems in many practical applications are solved much more efficiently. (C) 2007 Elsevier Inc. All rights reserved

On the choice of parameters in MAOR type splitting methods for the linear complementarity problem

In the present work we consider the iterative solution of the Linear Complementarity Problem (LCP), with a nonsingular H (+) coefficient matrix A, by using all modulus-based matrix splitting iterative methods that have been around for the last couple of years. A deeper analysis shows that the iterative solution of the LCP by the modified Accelerated Overrelaxation (MAOR) iterative method is the "best", in a sense made precise in the text, among all those that have been proposed so far regarding the following three issues: i) The positive diagonal matrix-parameter Omega a parts per thousand yen diag(A) involved in the method is Omega = diag(A), ii) The known convergence intervals for the two AOR parameters, alpha and beta, are the widest possible, and iii) The "best" possible MAOR iterative method is the modified Gauss-Seidel one